Abstract:
This paper is devoted to spectral synthesis of the operator adjoint to multiplication by a power of the independent variable in weighted spaces of entire functions of a single complex variable, and is closely connected with equations of convolution type, and with the general theory of subspaces invariant under a multiple differentiation operator. The problem of approximating solutions of a homogeneous equation of q-sided convolution type by elementary solutions is solved. Certain systems of such equations are investigated.
Citation:
A. B. Shishkin, “Spectral synthesis for an operator generated by multiplication by a power of the independent variable”, Math. USSR-Sb., 73:1 (1992), 211–229
\Bibitem{Shi91}
\by A.~B.~Shishkin
\paper Spectral synthesis for an operator generated by multiplication by a~power of the independent variable
\jour Math. USSR-Sb.
\yr 1992
\vol 73
\issue 1
\pages 211--229
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Linking options:
https://www.mathnet.ru/eng/sm1326
https://doi.org/10.1070/SM1992v073n01ABEH002542
https://www.mathnet.ru/eng/sm/v182/i6/p828
This publication is cited in the following 12 articles:
A. A. Tatarkin, A. B. Shishkin, “Exponential Synthesis in the Kernel of a q-Sided Convolution Operator”, J Math Sci, 282:4 (2024), 581
A. A. Tatarkin, A. B. Shishkin, “Eksponentsialnyi sintez v yadre operatora q-storonnei svertki”, Issledovaniya po lineinym operatoram i teorii funktsii. 50, Zap. nauchn. sem. POMI, 512, POMI, SPb., 2022, 191–222
Yu. S. Saranchuk, A. B. Shishkin, “General elementary solution of a homogeneous q-sided convolution type equation”, St. Petersburg Math. J., 34:4 (2023), 695–713
A. B. Shishkin, “On continuous endomorphisms of entire functions”, Sb. Math., 212:4 (2021), 567–591
A. A. Tatarkin, A. B. Shishkin, “Sintez v yadre operatora trekhstoronnei svertki”, Materialy Voronezhskoi vesennei matematicheskoi shkoly
«Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniya–XXX». Voronezh, 3–9 maya 2019 g. Chast 4, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 193, VINITI RAN, M., 2021, 130–141
A. B. Shishkin, “Symmetric representations of holomorphic functions”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 124–136
A. A. Tatarkin, U. S. Saranchuk, “Elementary solutions of a homogeneous q-sided convolution equation”, Probl. anal. Issues Anal., 7(25), spetsvypusk (2018), 137–152
A. B. Shishkin, “Exponential synthesis in the kernel of a symmetric convolution”, J. Math. Sci. (N. Y.), 229:5 (2018), 572–599
A. B. Shishkin, “Proektivnoe i in'ektivnoe opisaniya v kompleksnoi oblasti. Dvoistvennost”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 14:1 (2014), 47–65
T. A. Volkovaya, A. B. Shishkin, “Lokalnoe opisanie tselykh funktsii. Podmoduli ranga 1”, Vladikavk. matem. zhurn., 16:2 (2014), 14–28
A. B. Shishkin, “Spectral synthesis for systems of differential operators with
constant coefficients”, Sb. Math., 194:12 (2003), 1865–1898
I. F. Krasichkov-Ternovskii, “Spectral synthesis and local description for several variables”, Izv. Math., 63:4 (1999), 729–755
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